Simultaneous Replacement in Normal Programs

The simultaneous replacement transformation operation is here defined and studied w.r.t. normal programs. We give applicability conditions able to ensure the correctness of the operation w.r.t. the set of logical consequences of the completed database. We consider separately the cases in which the underlying language is infinite and finite; in this latter case we also distinguish according to the kind of domain closure axioms adopted. As corollaries we obtain results for Fitting's and Kunen's semantics. We also show how simultaneous replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too

Transformation of logic programs: Foundations and techniques

AbstractWe present an overview of some techniques which have been proposed for the transformation of logic programs. We consider the so-called “rules + strategies” approach, and we address the following two issues: the correctness of some basic transformation rules w.r.t. a given semantics and the use of strategies for guiding the application of the rules and improving efficiency. We will also show through some examples the use and the power of the transformational approach, and we will briefly illustrate its relationship to other methodologies for program development

On derived dependencies and connected databases

AbstractThis paper introduces a new class of deductive databases (connected databases) for which SLDNF-resolution never flounders and always computes ground answers. The class of connected databases properly includes that of allowed databases. Moreover the definition of connected databases enables evaluable predicates to be included in a uniform way. An algorithm is described which, for each predicate defined in a normal database, derives a propositional formula (groundness formula) describing dependencies between the arguments of that predicate. Groundness formulae are used to determine whether a database is connected. They are also used to identify goals for which SLDNF-resolution will never flounder and will always compute ground answers on a connected database

Tabling and Answer Subsumption for Reasoning on Logic Programs with Annotated Disjunctions

Abstract Probabilistic Logic Programming is an active field of research, with many proposals for languages, semantics and reasoning algorithms. One such proposal, Logic Programming with Annotated Disjunctions (LPADs) represents probabilistic information in a sound and simple way. This paper presents the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) for computing the probability of queries. Answer subsumption is a feature of tabling that allows the combination of different answers for the same subgoal in the case in which a partial order can be defined over them. We have applied it in our case since probabilistic explanations (stored as BDDs in PITA) possess a natural lattice structure. PITA has been implemented in XSB and compared with ProbLog, cplint and CVE. The results show that, in almost all cases, PITA is able to solve larger problems and is faster than competing algorithms

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Scalable Reasoning for Knowledge Bases Subject to Changes

ScienceWeb is a semantic web system that collects information about a research community and allows users to ask qualitative and quantitative questions related to that information using a reasoning engine. The more complete the knowledge base is, the more helpful answers the system will provide. As the size of knowledge base increases, scalability becomes a challenge for the reasoning system. As users make changes to the knowledge base and/or new information is collected, providing fast enough response time (ranging from seconds to a few minutes) is one of the core challenges for the reasoning system. There are two basic inference methods commonly used in first order logic: forward chaining and backward chaining. As a general rule, forward chaining is a good method for a static knowledge base and backward chaining is good for the more dynamic cases. The goal of this thesis was to design a hybrid reasoning architecture and develop a scalable reasoning system whose efficiency is able to meet the interaction requirements in a ScienceWeb system when facing a large and evolving knowledge base. Interposing a backward chaining reasoner between an evolving knowledge base and a query manager with support of trust yields an architecture that can support reasoning in the face of frequent changes. An optimized query-answering algorithm, an optimized backward chaining algorithm and a trust-based hybrid reasoning algorithm are three key algorithms in such an architecture. Collectively, these three algorithms are significant contributions to the field of backward chaining reasoners over ontologies. I explored the idea of trust in the trust-based hybrid reasoning algorithm, where each change to the knowledge base is analyzed as to what subset of the knowledge base is impacted by the change and could therefore contribute to incorrect inferences. I adopted greedy ordering and deferring joins in optimized query-answering algorithm. I introduced four optimizations in the algorithm for backward chaining. These optimizations are: 1) the implementation of the selection function, 2) the upgraded substitute function, 3) the application of OLDT and 4) solving of the owl: sameAs problem. I evaluated our optimization techniques by comparing the results with and without optimization techniques. I evaluated our optimized query answering algorithm by comparing to a traditional backward-chaining reasoner. I evaluated our trust-based hybrid reasoning algorithm by comparing the performance of a forward chaining algorithm to that of a pure backward chaining algorithm. The evaluation results have shown that the hybrid reasoning architecture with the scalable reasoning system is able to support scalable reasoning of ScienceWeb to answer qualitative questions effectively when facing both a fixed knowledge base and an evolving knowledge base